552 JOSEPH BARRELL 



masses which would exert a very appreciable effect if near the 

 surface would, in consequence, not betray their existence if situ- 

 ated near the base of the zone of compensation. But the larger 

 masses which are found to exist would exert a very visible control 

 upon the deflections of the vertical, even if their centers were at 

 a depth of 100-200 km. The fact that such depths have not been 

 found suggests that the larger variations from the mean density 

 within any one earth shell tend to occur in the outer half of the 

 zone of compensation rather than in its deeper parts or immedi- 

 ately below it. 



As a step toward the interpretation of the evidence, let the con- 

 clusion reached in Part II of this article be accepted: that regional 

 isostasy for ordinary relief certainly extends to a radius of 100 and 

 probably to 150 or 200 km. Even these hmits do not reach the 

 capacity of crustal strength. Such regional limits would not in 

 reality be subject to sharp boundaries. This agrees with the 

 evidence of geology in showing that mountain groups of circum- 

 denudation — those whose relief is due to erosion and not to origi- 

 nal differential vertical movement — are upheld by the rigidity of 

 the crust. This applies to many of the mountain groups of the 

 Appalachians; such, for example, as the Catskills. 



The fairest initial hj^pothesis of isostatic compensation would be 

 then to calculate for each station the average elevation of the 

 country within a radius of 99 km., being the outer radius of zone N, 

 and to assume a uniform density to these limits such as is needed to 

 compensate this area. A second trial hypothesis would be to use 

 as the radius of regional compensation the outer hmits of zone 0, 

 166.7 km. Under these two calculations for regional compensa- 

 tion the Catskills would be regarded as producing deflections 

 which should show an excess of mass at the surface of the earth. 

 Such an erosion basin as the Nashville basin should show, on the 

 other hand, by its deflections a surface deficiency of mass. For 

 the hypothesis which approaches nearest to the truth, the residuals 

 of the deflections should be small and the outstanding masses 

 would be determined by variations of density within the crust and 

 not of the topography upon its surface. 



Under the hypothesis of local compensation as given in Solution 

 H the excess of mass in the Catskills would show, on the contrary, 



